Question: Reduce to lowest terms: $ \dfrac{1}{7} \div - \dfrac{3}{4} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{3}{4}$ is $- \dfrac{4}{3}$ Therefore: $ \dfrac{1}{7} \div - \dfrac{3}{4} = \dfrac{1}{7} \times - \dfrac{4}{3} $ $ \phantom{ \dfrac{1}{7} \times - \dfrac{4}{3}} = \dfrac{1 \times -4}{7 \times 3} $ $ \phantom{ \dfrac{1}{7} \times - \dfrac{4}{3}} = \dfrac{-4}{21} $